How fast is the water level rising?

Question

A tank has the shape of a rectangular prism, three feet long and 2 feet wide. Water is being pumped in at a rate of 15 gallons every 4 minutes. Approximately how fast is the water level in the tank rising? (There are approximately 7.5 gallons in a cubic foot).

Answer 1

the volume of the water is increasing at 15 galons every 4 minutes.  15 gallons = 7.5gallon * 2 = 1ft³ * 2 = 2ft³

 

So the volume is increasing at 2ft³/4min = 0.5ft³/min

 

After t minutes, the volume is 0.5t

If the height of the water is h(t), then the volume of the water in the container is also given by: 2 x 3 x h(t) = 0.5t

 

 

So, the height of the water level is equal to 0.5*t/6 = t/12. ft

 

The rate at which the water level is therefore 1/12. ft/s